Container With Most Water

Info

🔗 https://leetcode.com/problems/container-with-most-water/description/

Description

You are given an integer array height of length n. There are n vertical lines drawn such that the two endpoints of the ith line are (i, 0) and (i, height[i]).

Find two lines that together with the x-axis form a container, such that the container contains the most water.

Return the maximum amount of water a container can store.

Notice that you may not slant the container.

Example 1:

img

Input: height = [1,8,6,2,5,4,8,3,7]
Output: 49
Explanation: The above vertical lines are represented by array [1,8,6,2,5,4,8,3,7]. In this case, the max area of water (blue section) the container can contain is 49.

Example 2:

Input: height = [1,1]
Output: 1

Constraints:

• n == height.length
• 2 <= n <= 105
• 0 <= height[i] <= 104

Solution

Violence(Overtime)

 public int maxArea(int[] height) {
        int final_max = 0;
        for(int i = 0; i < height.length; i++) {
            int max = 0;
            for(int j = 0; j < height.length; j++) {
                int min = Math.min(height[i], height[j]);
                int gap = Math.abs(i - j);
                max = Math.max(max, min*gap);
            }
            final_max = Math.max(final_max, max);
        }
        return final_max;
    }

Dual_Pointer (Copy)

• If the short plate is moved inward, the short plate min(h[i], h[j]) of the sink may become larger, so the area of the next sink may increase.
• If the long plate is moved inward, the short plate min(h[i], h[j]) of the sink will remain unchanged or become smaller, so the area of the next sink must become smaller.

class Solution {
    public int maxArea(int[] height) {
        int i = 0, j = height.length - 1, res = 0;
        while(i < j) {
            res = height[i] < height[j] ? 
                Math.max(res, (j - i) * height[i++]): 
                Math.max(res, (j - i) * height[j--]); 
        }
        return res;
    }
}

// 作者：Krahets
// 链接：https://leetcode.cn/problems/container-with-most-water/solutions/11491/container-with-most-water-shuang-zhi-zhen-fa-yi-do/